I think start walking for half an hour a day, as briskly as you can manage, your fitness will still build up. Running may be a bridge too far yet, I know I find running a struggle at 13 stone odd, even though I'm an experienced runner. A stone less has made all the difference. If you can run - great, but don't beat yourself up if it's too hard. Low impact exercise which gets your heart rate up a bit would be the best thing just now, IMO.
Actually I think it would be good idea to ask for a fitness monitor band for Christmas, then you will be able to see your progress. Also having a FitBit helped me to see how many steps slim friends do - a lot more than I was doing!
While exercise is important for your heart you really need to spend much of your focus on diet and what you drink. I'd say go to your doctor anyway to get cholesterol, blood sugar and blood pressure checked and get their advice. If you can, also see a dietician- will probably cost about £100 for initial consultation, but one visit was enough for me to set me on the right track. You could easily spend that at WW or Slimming World.
Cutting back on snacks and alcohol (if you drink) will probably make an immediate difference. One tip my dietician said to me was to make your evening meal (on a 10" plate) 25% lean protein 25% carbs and 50% veg - it made me instantly cut my portion sizes.
Whatever you do has to be a long term and sustainable change of habits rather than a diet from which most people will rebound. And don't worry if you slip up along the way, see it as a long journey. Set yourself short term goals.
I started off calorie counting and using MyFitnessPal. Managed that for 3 months and got fed up, but I think it was useful for a time to reset portion control. I'm now doing 5:2, which I've been doing for several months and I find it very sustainable and even enjoyable. I've gone from BMI 31.5 to 27. More to go yet, but I'm enjoying being able to walk into a shop and know that a size 14 will definitely fit, or even be a bit loose, rather than wondering whether a size 18 will fit or at all look good. But find what works for you. Good luck.